In an industrial environment, manufacturing systems may be subject to considerable uncertainties which could lead to numerous schedule disturbances. These disturbances prevent the execution of a manufacturing schedule as it was planned. The "groups of permutable operations" method copes with this drawback by proposing a family of schedules instead of a unique one. However, the selection of the appropriate schedule that accounts for real-time disturbances, represents a combinatorial optimization challenge. In this paper, we propose a new decision-aid criterion for selecting the schedule that fits best the real state of the shop. This criterion is measured using a greedy heuristic that anticipates the maximum tardiness in a job shop scheduling environment. Simulation tests performed on benchmark problems show the usefulness of the proposed criterion compared to another frequently used criterion. The final results emphasize the usefulness of this criterion in a bi-criteria decision-aid system.